Chapter 3 Projectile Motion
3.1 Vector and Scalar Quantities
Scalar Quantity – Measurement that shows only magnitude.
Vector Quantity – Measurement that shows both magnitude and direction.
3.2 Velocity Vectors
Vectors are simply arrows used to represent the magnitude and direction of motion.
The length of the arrow drawn shows the size or magnitude of the velocity (speed) and the head of the arrow shows the direction of the motion.
100 m/s East
Resultant Vector - Vector that results from a combination of two or more vectors placed together.
Example 1:
What if a plane traveling at 100 m/s E encounters a tail wind that is moving at 20 m/s E. How fast will the plane be traveling now?
r
20 m/s 100 m/s
Example 2:
What if a plane traveling at 100 m/s E encounters a tail wind that is moving at 20 m/s E. How fast will the plane be traveling now?
r 20 m/s
100 m/s
Example 3:
Let’s say that same airplane traveling at 100 m/s eastward is subjected to a cross wind of 20 m/s in a northward direction. What is the resultant velocity of the plane in reference to the ground?
Step 1 – Drawing the vector diagram.
r
20 m/s
100 m/s
Step 2 – Calculating the resultant velocity and angle of movement.
To find the velocity: Use a2 + b2 = c2
202 + 1002 = r2
10400 = r2
√10400 = r
102 m/s = r
To find the angle of the motion: Use either sine, cosine, or tangent functions on your calculator:
Using Sin A = 20 m/s / 100 m/s = .200
The angle A is found by taking the inverse sine ( Sin –1) of .200.
This produces 11.3 degrees
SO, the direction of the motion is 11.3 degrees North of East